Violation of classical inequalities by photon frequency-filtering

The violation of the Cauchy-Schwarz and Bell inequalities ranks among the major evidences of the genuinely quantum nature of an emitter. We show that by dispensing from the usual approximation of mode correlations and studying directly correlations between the physical reality -the photons- these violations can be optimized. This is achieved by extending the concept of photon correlations to all frequencies in all the possible windows of detections, with no prejudice to the supposed origin of the photons. We identify the regions of quantum emission as rooted in collective de-excitation involving virtual states instead of, as previously assumed, cascaded transitions between real states.